MODELLING AND DYNAMIC STABILISATION OF A COMPLIANT HUMANOID ROBOT, CoMan

This dissertation presents the results of a series of studies on dynamic stabilisation of CoMan, which is actuated by series elastic actuators. The main goal of this dissertation is to dynamically stabilise the humanoid robot on the floor by the simplest multivariate feedback control for the purpose of walking. The multivariable scheme is chosen to take into account the joints' interactions, as well as providing a systematic way of designing the feedback system to improve the bandwidth and tracking performance of CoMan's existing PID control. A detailed model is derived which includes all the motors and joints state variables and their multibody interactions which are often ignored in the previous studies on bipedal robots in the literature. The derived dynamic model is then used to design multivariable optimal control feedback and observers with a mathematical proof for the relative stability and robustness of the closed loop system in face of model uncertainties and disturbances. In addition, two decentralized optimal feedback design algorithms are presented that explicitly take the compliant dynamics and the multibody interactions into account while providing the mathematical proof for the stability of the overall system. The purpose of the proposed decentralized control methods is to provide a systematic model based PD-PID design to replace the existing PID controllers which are derived by a trial and error process. Moreover, the challenging constrained and compliant motion of the robot in double support is studied where a novel constrained feedback design is proposed which directly takes the compliance dynamics, interactions and the constraints into account to provide a closed loop feedback tracking system that drives the robot inside the constrained subspace. This method of control is particularly interesting since most control methods applied to closed kinematic chains (such as the double support phase) are over complicated for implementation purposes or have an ad-hoc approach to controller design. In terms of walking trajectory generation, an extension to the ZMP walking trajectory generation is proposed to utilise the CoMan's upper body to tackle the non-minimum phase behaviour that is faced in trajectory generation. Simple inverted pendulum models of walking are then used to study the maximum feasible walking speed and step size where parameters of CoMan are used to provide numerical upper-bounds on the step size and walking speed. Use of straight knee and toe push-off during walking is shown to be beneficial for taking larger step lengths and hence achieving faster walking speeds. Subsequently, the designed tracking systems are then applied to a dynamic walking simulator which is developed during this PhD project to accurately model the compliant walking behaviour of the CoMan. A walking gait is simulated and visualized to show the effectiveness of the developed walking simulator. Moreover, the experimental results and challenges faced during the implementation of the designed tracking control systems are discussed where it is shown that the LQR feedback results in 50\% less control effort and tracking errors in comparison with CoMan's existing independent PID control. This advantage directly affects the feasible walking speed. In addition, a set of standard and repeatable tests for CoMan are designed to quantify and compare the performance of various control system designs. Finally, the conclusions and future directions are pointed out